Question

In Python 3.6

Classes and Methods: A class for estimating the derivative of a function f) at the form: takes where h is a small change in x. The goal of this exercise is to use the formula above to differentinte a mat hematical function f(x) implemented as a Python function f(x) Implement class Diff with two special methods. The--init--() method takes in function object and also an optional argument h. The default value of h is le-4. Implement also the special method call so that the instance is callable. This method returns the approximation of the derivative of the funetion using the formula ahove. The following code shows you how this class can be used to compare the exact value of the derivative versus its approximation for the function f(r) = (1 /4)r'. def f(x) return 0.25x**4 df Diff(f) # make function-like object df " # df (%) computes the derivative of f(z) approzi«ately: for x in [.5, 101: d1.value dt (x) # appro# V4tue of derivative of ! at Point # 4 ezact vale of derivative df.value)) The following are test cases for the derivative of f()In(x), evaluated at r various values of h Test Cases: Test case 1 10 for Input Output: (0.09950330853167877, 0.000496691468321 2365) # derivative, approxi- mation erro Test case 2 x = 10.0, f = log, h = 0.5, Input Output: (0.09758032833886343, 0.0024196716611365743) Test case 3 10.0, f = log, h 1.0E-5, Input Output: (0.09999994996512383, 5.003487617283309e-08) x Test case 4 10.0, f= log, h = 1.0E-9. Input Output: (0.1000000082740371, -8.274037094357922e-09) Test case 5 x-10.0, f= log, h = 1.0E-11, Input Output: (0.0999644811372491, 3.551886275091065e-05)

Answer 1

Code for the implementation of class Diff:

import math

class Diff:
def __init__(self,f,h=math.exp(-4)):
self.f=f;
self.h=h;
  
def __call__(self,x):
return (self.f(x+self.h)-self.f(x))/self.h;

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